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Full text of "Text Book Of Mechanical Engineering"

856

Appendix II.

Let lines a and b be tangents to the curve at A and B respec-
tively.    Then 0 = a, and tan a = a, as a is small.    Also  -

I>=j;0=J'tt==:j/ tana

and 7 r>'= ty tana = Ejy (slope accumulated from A to B)

Let Q H j be a Bm curve for the bad, which we can transform
into a limiting-stress curve, for/= Bm^-Z.    Then

/D = area M = (slope accumulated from A to B) Ey

also,  area NT == (slope accumulated from B to c) Ey

.-,  areas M-F-N- = (slope accumulated from A toe) Ey.

Hence,     sum of stress    ,11 total slope at )' *
curve to any point )       (   that point    J  ?